It seems to me that there is a perception on the part of some in the "never crop" camp that cropping is somehow a sign of sloppiness or lack of artistic rigor. The "integrity" (artistic or otherwise) of cropped images has even been called into question.
While I'm sure there are some for whom cropping is a shortcut, there are many of us who crop regularly and who hold ourselves to the strictest personal standards. Cropping is, in these cases, an integral part of the way the photographer works, and based on a clear vision of the desired end result. I'll elaborate some of my reasons again, using a different approach.
Although I respect those who commit themselves to working in only one or two given aspect ratios, dictated by the film format(s) they use, and who try to compose each shot to its fullest within those constraints (usually these are photographers who use smaller formats), I work differently. The aspect ratios of my photographs are rarely the same; they are subject-driven and determined carefully and (hopefully) insightfully to best portray the subjects with the most possible impact and to communicate the emotions that I want. Personally, I would hate being constrained by a 4x5 aspect ratio (even though that's what I shoot) and even more so 5x7 or 24x35...
So, I crop to get the aspect ratio I desire; there is no other way to achieve this tailoring of aspect ratio to subject.
Perspective is determined by camera position. Finding the right spot to place my camera for a shot takes most of my creative time when making an image. However, after determining camera position and the framing I want (see above), I rarely have a lens that will let me take full advantage of the negative area; I need to use the next-shorter focal length I have with me from "ideal" (which may be a length that isn't even manufactured). Let me stress that moving closer is not an option in this case; it would change the perspective I have so carefully chosen to begin with. (An aside here: with 35mm cameras and zoom lenses, this is much less of an issue. One can frame to any focal length in the zoom range. For those of us who are constrained to use prime lenses and who, for whatever reason, don't always carry every commercially-available focal length with them at all times, shooting looser and cropping later is the only practical solution.)
So, I crop to keep the perspective I desire; there is no other way to achieve this with the lens selection I have with me.
Even though I crop regularly, I always have a clear idea of how I want to present the image I'm working on with regard to aspect ratio and perspective. That's enough artistic integrity for me

I'm not about to compromise my intentions for a particular image to the aspect ratio of the film I happen to be working with or the lens selection I have. However, and especially when shooting under time constraints, in inclement weather or in low-light, the best laid plans of mice and men (me included) do oftimes go astray: Sometimes I can't achieve exactly what I want under the circumstances and, yes (horrors!) I will compromise by shooting loose and cropping-to-compose later. I have the luxury of a bit more film area than 35mm and MF, so this is a viable approach technically, even though it is often a bit of a "Hail Mary." That said, every now and then the "Hail Mary" works; if not, the negative goes into the reject pile with the hundreds of other (more carefully considered and executed) rejects.
So, I crop to compensate for compromising during difficult conditions when photographing; maybe I could have done better, but chose not to since it makes no appreciable difference on the final image. (There goes my integrity...)
Best,
Doremus